Whewww that website looks pretty sketchy to me hahaha but no harm in trying, thanks for the suggestion.
I guess you could get your hands on an used DS for cheap nowadays. That'd be your best bet.
I've been migrating some Slakoths all the way from Sapphire today, and I realized how much better Gen transfers have been getting over time...
Gen 3 -> Gen 4 was a ridiculous pain in the ass, limiting you to six pokémon
per day, and you'd even have to catch them in your Gen 4 game in some awful mockery of the Safari Zone, where you had to look for each one of them in different areas, depending on the pokémon; at least your only option was to throw insta-capture pokéballs.
Gen 4 -> Gen 5 still forced you to play a boring mini-game, but at least it was a whole lot faster and had no daily cap
Gen 5 -> Gen 6 finally could be done using a single 3DS system, didn't force you to play a boring mini-game to do the transfer, and even let you transfer a whole box at once. I only wish they'd let you select which box to transfer rather than forcing you to boot up your Gen 5 game over and over to move whichever pokémon you want to transfer to Box 1